Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,4,Mod(649,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.649");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(79.6525785077\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 270) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.649 |
Dual form | 1350.4.c.d.649.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.00000i | 0.215980i | 0.994152 | + | 0.107990i | \(0.0344414\pi\) | ||||
−0.994152 | + | 0.107990i | \(0.965559\pi\) | |||||||
\(8\) | − 8.00000i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −42.0000 | −1.15123 | −0.575613 | − | 0.817723i | \(-0.695236\pi\) | ||||
−0.575613 | + | 0.817723i | \(0.695236\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 20.0000i | 0.426692i | 0.976977 | + | 0.213346i | \(0.0684362\pi\) | ||||
−0.976977 | + | 0.213346i | \(0.931564\pi\) | |||||||
\(14\) | −8.00000 | −0.152721 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 93.0000i | 1.32681i | 0.748259 | + | 0.663406i | \(0.230890\pi\) | ||||
−0.748259 | + | 0.663406i | \(0.769110\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −59.0000 | −0.712396 | −0.356198 | − | 0.934410i | \(-0.615927\pi\) | ||||
−0.356198 | + | 0.934410i | \(0.615927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 84.0000i | − 0.814039i | ||||||||
\(23\) | − 9.00000i | − 0.0815926i | −0.999167 | − | 0.0407963i | \(-0.987011\pi\) | ||||
0.999167 | − | 0.0407963i | \(-0.0129895\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −40.0000 | −0.301717 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 16.0000i | − 0.107990i | ||||||||
\(29\) | 120.000 | 0.768395 | 0.384197 | − | 0.923251i | \(-0.374478\pi\) | ||||
0.384197 | + | 0.923251i | \(0.374478\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 47.0000 | 0.272305 | 0.136152 | − | 0.990688i | \(-0.456526\pi\) | ||||
0.136152 | + | 0.990688i | \(0.456526\pi\) | |||||||
\(32\) | 32.0000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −186.000 | −0.938198 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 262.000i | 1.16412i | 0.813145 | + | 0.582061i | \(0.197754\pi\) | ||||
−0.813145 | + | 0.582061i | \(0.802246\pi\) | |||||||
\(38\) | − 118.000i | − 0.503740i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −126.000 | −0.479949 | −0.239974 | − | 0.970779i | \(-0.577139\pi\) | ||||
−0.239974 | + | 0.970779i | \(0.577139\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 178.000i | − 0.631273i | −0.948880 | − | 0.315637i | \(-0.897782\pi\) | ||||
0.948880 | − | 0.315637i | \(-0.102218\pi\) | |||||||
\(44\) | 168.000 | 0.575613 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 18.0000 | 0.0576947 | ||||||||
\(47\) | 144.000i | 0.446906i | 0.974715 | + | 0.223453i | \(0.0717328\pi\) | ||||
−0.974715 | + | 0.223453i | \(0.928267\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 327.000 | 0.953353 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 80.0000i | − 0.213346i | ||||||||
\(53\) | − 741.000i | − 1.92046i | −0.279217 | − | 0.960228i | \(-0.590075\pi\) | ||||
0.279217 | − | 0.960228i | \(-0.409925\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 32.0000 | 0.0763604 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 240.000i | 0.543337i | ||||||||
\(59\) | −444.000 | −0.979727 | −0.489863 | − | 0.871799i | \(-0.662953\pi\) | ||||
−0.489863 | + | 0.871799i | \(0.662953\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 221.000 | 0.463871 | 0.231936 | − | 0.972731i | \(-0.425494\pi\) | ||||
0.231936 | + | 0.972731i | \(0.425494\pi\) | |||||||
\(62\) | 94.0000i | 0.192549i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 538.000i | 0.981002i | 0.871441 | + | 0.490501i | \(0.163186\pi\) | ||||
−0.871441 | + | 0.490501i | \(0.836814\pi\) | |||||||
\(68\) | − 372.000i | − 0.663406i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −690.000 | −1.15335 | −0.576676 | − | 0.816973i | \(-0.695650\pi\) | ||||
−0.576676 | + | 0.816973i | \(0.695650\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 1126.00i | − 1.80532i | −0.430355 | − | 0.902660i | \(-0.641612\pi\) | ||||
0.430355 | − | 0.902660i | \(-0.358388\pi\) | |||||||
\(74\) | −524.000 | −0.823159 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 236.000 | 0.356198 | ||||||||
\(77\) | − 168.000i | − 0.248641i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −665.000 | −0.947068 | −0.473534 | − | 0.880776i | \(-0.657022\pi\) | ||||
−0.473534 | + | 0.880776i | \(0.657022\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 252.000i | − 0.339375i | ||||||||
\(83\) | − 75.0000i | − 0.0991846i | −0.998770 | − | 0.0495923i | \(-0.984208\pi\) | ||||
0.998770 | − | 0.0495923i | \(-0.0157922\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 356.000 | 0.446378 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 336.000i | 0.407020i | ||||||||
\(89\) | −1086.00 | −1.29344 | −0.646718 | − | 0.762729i | \(-0.723859\pi\) | ||||
−0.646718 | + | 0.762729i | \(0.723859\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −80.0000 | −0.0921569 | ||||||||
\(92\) | 36.0000i | 0.0407963i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −288.000 | −0.316010 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1544.00i | − 1.61618i | −0.589059 | − | 0.808090i | \(-0.700501\pi\) | ||||
0.589059 | − | 0.808090i | \(-0.299499\pi\) | |||||||
\(98\) | 654.000i | 0.674122i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 132.000 | 0.130044 | 0.0650222 | − | 0.997884i | \(-0.479288\pi\) | ||||
0.0650222 | + | 0.997884i | \(0.479288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 892.000i | − 0.853314i | −0.904413 | − | 0.426657i | \(-0.859691\pi\) | ||||
0.904413 | − | 0.426657i | \(-0.140309\pi\) | |||||||
\(104\) | 160.000 | 0.150859 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1482.00 | 1.35797 | ||||||||
\(107\) | − 1140.00i | − 1.02998i | −0.857196 | − | 0.514990i | \(-0.827795\pi\) | ||||
0.857196 | − | 0.514990i | \(-0.172205\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1735.00 | 1.52461 | 0.762307 | − | 0.647216i | \(-0.224067\pi\) | ||||
0.762307 | + | 0.647216i | \(0.224067\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 64.0000i | 0.0539949i | ||||||||
\(113\) | 1434.00i | 1.19380i | 0.802316 | + | 0.596900i | \(0.203601\pi\) | ||||
−0.802316 | + | 0.596900i | \(0.796399\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −480.000 | −0.384197 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 888.000i | − 0.692771i | ||||||||
\(119\) | −372.000 | −0.286565 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 433.000 | 0.325319 | ||||||||
\(122\) | 442.000i | 0.328007i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −188.000 | −0.136152 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 686.000i | − 0.479312i | −0.970858 | − | 0.239656i | \(-0.922965\pi\) | ||||
0.970858 | − | 0.239656i | \(-0.0770347\pi\) | |||||||
\(128\) | − 128.000i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 114.000 | 0.0760323 | 0.0380161 | − | 0.999277i | \(-0.487896\pi\) | ||||
0.0380161 | + | 0.999277i | \(0.487896\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 236.000i | − 0.153863i | ||||||||
\(134\) | −1076.00 | −0.693673 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 744.000 | 0.469099 | ||||||||
\(137\) | 159.000i | 0.0991554i | 0.998770 | + | 0.0495777i | \(0.0157875\pi\) | ||||
−0.998770 | + | 0.0495777i | \(0.984212\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2276.00 | −1.38883 | −0.694417 | − | 0.719573i | \(-0.744337\pi\) | ||||
−0.694417 | + | 0.719573i | \(0.744337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 1380.00i | − 0.815542i | ||||||||
\(143\) | − 840.000i | − 0.491219i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2252.00 | 1.27655 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 1048.00i | − 0.582061i | ||||||||
\(149\) | −1398.00 | −0.768648 | −0.384324 | − | 0.923198i | \(-0.625566\pi\) | ||||
−0.384324 | + | 0.923198i | \(0.625566\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2624.00 | 1.41416 | 0.707080 | − | 0.707134i | \(-0.250012\pi\) | ||||
0.707080 | + | 0.707134i | \(0.250012\pi\) | |||||||
\(152\) | 472.000i | 0.251870i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 336.000 | 0.175816 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 394.000i | 0.200284i | 0.994973 | + | 0.100142i | \(0.0319297\pi\) | ||||
−0.994973 | + | 0.100142i | \(0.968070\pi\) | |||||||
\(158\) | − 1330.00i | − 0.669678i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 36.0000 | 0.0176223 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 3346.00i | − 1.60785i | −0.594733 | − | 0.803923i | \(-0.702742\pi\) | ||||
0.594733 | − | 0.803923i | \(-0.297258\pi\) | |||||||
\(164\) | 504.000 | 0.239974 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 150.000 | 0.0701341 | ||||||||
\(167\) | − 1491.00i | − 0.690881i | −0.938441 | − | 0.345440i | \(-0.887730\pi\) | ||||
0.938441 | − | 0.345440i | \(-0.112270\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1797.00 | 0.817934 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 712.000i | 0.315637i | ||||||||
\(173\) | − 2403.00i | − 1.05605i | −0.849229 | − | 0.528025i | \(-0.822933\pi\) | ||||
0.849229 | − | 0.528025i | \(-0.177067\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −672.000 | −0.287806 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 2172.00i | − 0.914597i | ||||||||
\(179\) | −2640.00 | −1.10236 | −0.551181 | − | 0.834386i | \(-0.685823\pi\) | ||||
−0.551181 | + | 0.834386i | \(0.685823\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1073.00 | 0.440638 | 0.220319 | − | 0.975428i | \(-0.429290\pi\) | ||||
0.220319 | + | 0.975428i | \(0.429290\pi\) | |||||||
\(182\) | − 160.000i | − 0.0651648i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −72.0000 | −0.0288473 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3906.00i | − 1.52746i | ||||||||
\(188\) | − 576.000i | − 0.223453i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1470.00 | −0.556887 | −0.278444 | − | 0.960453i | \(-0.589819\pi\) | ||||
−0.278444 | + | 0.960453i | \(0.589819\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 4720.00i | − 1.76038i | −0.474623 | − | 0.880189i | \(-0.657416\pi\) | ||||
0.474623 | − | 0.880189i | \(-0.342584\pi\) | |||||||
\(194\) | 3088.00 | 1.14281 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1308.00 | −0.476676 | ||||||||
\(197\) | − 765.000i | − 0.276670i | −0.990385 | − | 0.138335i | \(-0.955825\pi\) | ||||
0.990385 | − | 0.138335i | \(-0.0441751\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −668.000 | −0.237956 | −0.118978 | − | 0.992897i | \(-0.537962\pi\) | ||||
−0.118978 | + | 0.992897i | \(0.537962\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 264.000i | 0.0919553i | ||||||||
\(203\) | 480.000i | 0.165958i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1784.00 | 0.603384 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 320.000i | 0.106673i | ||||||||
\(209\) | 2478.00 | 0.820128 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4601.00 | 1.50117 | 0.750583 | − | 0.660777i | \(-0.229773\pi\) | ||||
0.750583 | + | 0.660777i | \(0.229773\pi\) | |||||||
\(212\) | 2964.00i | 0.960228i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2280.00 | 0.728307 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 188.000i | 0.0588123i | ||||||||
\(218\) | 3470.00i | 1.07806i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1860.00 | −0.566141 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 2158.00i | − 0.648029i | −0.946052 | − | 0.324014i | \(-0.894967\pi\) | ||||
0.946052 | − | 0.324014i | \(-0.105033\pi\) | |||||||
\(224\) | −128.000 | −0.0381802 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2868.00 | −0.844144 | ||||||||
\(227\) | 3123.00i | 0.913131i | 0.889690 | + | 0.456566i | \(0.150921\pi\) | ||||
−0.889690 | + | 0.456566i | \(0.849079\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2027.00 | −0.584925 | −0.292463 | − | 0.956277i | \(-0.594475\pi\) | ||||
−0.292463 | + | 0.956277i | \(0.594475\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 960.000i | − 0.271668i | ||||||||
\(233\) | 438.000i | 0.123152i | 0.998102 | + | 0.0615758i | \(0.0196126\pi\) | ||||
−0.998102 | + | 0.0615758i | \(0.980387\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1776.00 | 0.489863 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 744.000i | − 0.202632i | ||||||||
\(239\) | 6414.00 | 1.73593 | 0.867965 | − | 0.496626i | \(-0.165428\pi\) | ||||
0.867965 | + | 0.496626i | \(0.165428\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3431.00 | 0.917055 | 0.458527 | − | 0.888680i | \(-0.348377\pi\) | ||||
0.458527 | + | 0.888680i | \(0.348377\pi\) | |||||||
\(242\) | 866.000i | 0.230035i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −884.000 | −0.231936 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1180.00i | − 0.303974i | ||||||||
\(248\) | − 376.000i | − 0.0962743i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7308.00 | −1.83776 | −0.918878 | − | 0.394541i | \(-0.870904\pi\) | ||||
−0.918878 | + | 0.394541i | \(0.870904\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 378.000i | 0.0939314i | ||||||||
\(254\) | 1372.00 | 0.338925 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | − 3729.00i | − 0.905092i | −0.891741 | − | 0.452546i | \(-0.850516\pi\) | ||||
0.891741 | − | 0.452546i | \(-0.149484\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1048.00 | −0.251427 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 228.000i | 0.0537629i | ||||||||
\(263\) | 1956.00i | 0.458601i | 0.973356 | + | 0.229301i | \(0.0736439\pi\) | ||||
−0.973356 | + | 0.229301i | \(0.926356\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 472.000 | 0.108798 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 2152.00i | − 0.490501i | ||||||||
\(269\) | 990.000 | 0.224392 | 0.112196 | − | 0.993686i | \(-0.464212\pi\) | ||||
0.112196 | + | 0.993686i | \(0.464212\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8495.00 | 1.90419 | 0.952093 | − | 0.305808i | \(-0.0989266\pi\) | ||||
0.952093 | + | 0.305808i | \(0.0989266\pi\) | |||||||
\(272\) | 1488.00i | 0.331703i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −318.000 | −0.0701134 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1366.00i | 0.296300i | 0.988965 | + | 0.148150i | \(0.0473318\pi\) | ||||
−0.988965 | + | 0.148150i | \(0.952668\pi\) | |||||||
\(278\) | − 4552.00i | − 0.982053i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5520.00 | −1.17187 | −0.585935 | − | 0.810358i | \(-0.699273\pi\) | ||||
−0.585935 | + | 0.810358i | \(0.699273\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5438.00i | 1.14225i | 0.820865 | + | 0.571123i | \(0.193492\pi\) | ||||
−0.820865 | + | 0.571123i | \(0.806508\pi\) | |||||||
\(284\) | 2760.00 | 0.576676 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1680.00 | 0.347344 | ||||||||
\(287\) | − 504.000i | − 0.103659i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3736.00 | −0.760432 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4504.00i | 0.902660i | ||||||||
\(293\) | 8253.00i | 1.64555i | 0.568369 | + | 0.822774i | \(0.307575\pi\) | ||||
−0.568369 | + | 0.822774i | \(0.692425\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2096.00 | 0.411579 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 2796.00i | − 0.543517i | ||||||||
\(299\) | 180.000 | 0.0348149 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 712.000 | 0.136342 | ||||||||
\(302\) | 5248.00i | 0.999962i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −944.000 | −0.178099 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 9290.00i | − 1.72706i | −0.504295 | − | 0.863531i | \(-0.668248\pi\) | ||||
0.504295 | − | 0.863531i | \(-0.331752\pi\) | |||||||
\(308\) | 672.000i | 0.124321i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8112.00 | 1.47907 | 0.739533 | − | 0.673121i | \(-0.235047\pi\) | ||||
0.739533 | + | 0.673121i | \(0.235047\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 7900.00i | − 1.42663i | −0.700845 | − | 0.713314i | \(-0.747193\pi\) | ||||
0.700845 | − | 0.713314i | \(-0.252807\pi\) | |||||||
\(314\) | −788.000 | −0.141622 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2660.00 | 0.473534 | ||||||||
\(317\) | − 4419.00i | − 0.782952i | −0.920188 | − | 0.391476i | \(-0.871965\pi\) | ||||
0.920188 | − | 0.391476i | \(-0.128035\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5040.00 | −0.884595 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 72.0000i | 0.0124609i | ||||||||
\(323\) | − 5487.00i | − 0.945216i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6692.00 | 1.13692 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1008.00i | 0.169687i | ||||||||
\(329\) | −576.000 | −0.0965225 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8200.00 | −1.36167 | −0.680835 | − | 0.732437i | \(-0.738383\pi\) | ||||
−0.680835 | + | 0.732437i | \(0.738383\pi\) | |||||||
\(332\) | 300.000i | 0.0495923i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2982.00 | 0.488526 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9556.00i | 1.54465i | 0.635225 | + | 0.772327i | \(0.280907\pi\) | ||||
−0.635225 | + | 0.772327i | \(0.719093\pi\) | |||||||
\(338\) | 3594.00i | 0.578366i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1974.00 | −0.313484 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2680.00i | 0.421885i | ||||||||
\(344\) | −1424.00 | −0.223189 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4806.00 | 0.746740 | ||||||||
\(347\) | − 10116.0i | − 1.56500i | −0.622650 | − | 0.782500i | \(-0.713944\pi\) | ||||
0.622650 | − | 0.782500i | \(-0.286056\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6751.00 | 1.03545 | 0.517726 | − | 0.855546i | \(-0.326779\pi\) | ||||
0.517726 | + | 0.855546i | \(0.326779\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 1344.00i | − 0.203510i | ||||||||
\(353\) | 4062.00i | 0.612460i | 0.951958 | + | 0.306230i | \(0.0990677\pi\) | ||||
−0.951958 | + | 0.306230i | \(0.900932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4344.00 | 0.646718 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 5280.00i | − 0.779488i | ||||||||
\(359\) | −8778.00 | −1.29049 | −0.645244 | − | 0.763977i | \(-0.723244\pi\) | ||||
−0.645244 | + | 0.763977i | \(0.723244\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3378.00 | −0.492492 | ||||||||
\(362\) | 2146.00i | 0.311578i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 320.000 | 0.0460785 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 956.000i | − 0.135975i | −0.997686 | − | 0.0679875i | \(-0.978342\pi\) | ||||
0.997686 | − | 0.0679875i | \(-0.0216578\pi\) | |||||||
\(368\) | − 144.000i | − 0.0203981i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2964.00 | 0.414780 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2300.00i | 0.319275i | 0.987176 | + | 0.159637i | \(0.0510325\pi\) | ||||
−0.987176 | + | 0.159637i | \(0.948968\pi\) | |||||||
\(374\) | 7812.00 | 1.08008 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1152.00 | 0.158005 | ||||||||
\(377\) | 2400.00i | 0.327868i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.0000 | −0.00393042 | −0.00196521 | − | 0.999998i | \(-0.500626\pi\) | ||||
−0.00196521 | + | 0.999998i | \(0.500626\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 2940.00i | − 0.393779i | ||||||||
\(383\) | 8127.00i | 1.08426i | 0.840296 | + | 0.542128i | \(0.182381\pi\) | ||||
−0.840296 | + | 0.542128i | \(0.817619\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9440.00 | 1.24478 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6176.00i | 0.808090i | ||||||||
\(389\) | 7938.00 | 1.03463 | 0.517317 | − | 0.855794i | \(-0.326931\pi\) | ||||
0.517317 | + | 0.855794i | \(0.326931\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 837.000 | 0.108258 | ||||||||
\(392\) | − 2616.00i | − 0.337061i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1530.00 | 0.195635 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 272.000i | − 0.0343861i | −0.999852 | − | 0.0171931i | \(-0.994527\pi\) | ||||
0.999852 | − | 0.0171931i | \(-0.00547299\pi\) | |||||||
\(398\) | − 1336.00i | − 0.168260i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4554.00 | 0.567122 | 0.283561 | − | 0.958954i | \(-0.408484\pi\) | ||||
0.283561 | + | 0.958954i | \(0.408484\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 940.000i | 0.116190i | ||||||||
\(404\) | −528.000 | −0.0650222 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −960.000 | −0.117350 | ||||||||
\(407\) | − 11004.0i | − 1.34017i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1001.00 | −0.121018 | −0.0605089 | − | 0.998168i | \(-0.519272\pi\) | ||||
−0.0605089 | + | 0.998168i | \(0.519272\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3568.00i | 0.426657i | ||||||||
\(413\) | − 1776.00i | − 0.211601i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −640.000 | −0.0754293 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4956.00i | 0.579918i | ||||||||
\(419\) | 1794.00 | 0.209171 | 0.104585 | − | 0.994516i | \(-0.466648\pi\) | ||||
0.104585 | + | 0.994516i | \(0.466648\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16129.0 | −1.86717 | −0.933586 | − | 0.358354i | \(-0.883338\pi\) | ||||
−0.933586 | + | 0.358354i | \(0.883338\pi\) | |||||||
\(422\) | 9202.00i | 1.06148i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5928.00 | −0.678984 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 884.000i | 0.100187i | ||||||||
\(428\) | 4560.00i | 0.514990i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13356.0 | −1.49266 | −0.746329 | − | 0.665577i | \(-0.768186\pi\) | ||||
−0.746329 | + | 0.665577i | \(0.768186\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 11500.0i | − 1.27634i | −0.769896 | − | 0.638169i | \(-0.779692\pi\) | ||||
0.769896 | − | 0.638169i | \(-0.220308\pi\) | |||||||
\(434\) | −376.000 | −0.0415866 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6940.00 | −0.762307 | ||||||||
\(437\) | 531.000i | 0.0581263i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11149.0 | 1.21210 | 0.606051 | − | 0.795426i | \(-0.292753\pi\) | ||||
0.606051 | + | 0.795426i | \(0.292753\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 3720.00i | − 0.400322i | ||||||||
\(443\) | 3849.00i | 0.412803i | 0.978467 | + | 0.206401i | \(0.0661752\pi\) | ||||
−0.978467 | + | 0.206401i | \(0.933825\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4316.00 | 0.458225 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 256.000i | − 0.0269975i | ||||||||
\(449\) | −18048.0 | −1.89697 | −0.948483 | − | 0.316828i | \(-0.897382\pi\) | ||||
−0.948483 | + | 0.316828i | \(0.897382\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5292.00 | 0.552529 | ||||||||
\(452\) | − 5736.00i | − 0.596900i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6246.00 | −0.645681 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4264.00i | 0.436458i | 0.975898 | + | 0.218229i | \(0.0700280\pi\) | ||||
−0.975898 | + | 0.218229i | \(0.929972\pi\) | |||||||
\(458\) | − 4054.00i | − 0.413605i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10242.0 | −1.03475 | −0.517373 | − | 0.855760i | \(-0.673090\pi\) | ||||
−0.517373 | + | 0.855760i | \(0.673090\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3302.00i | 0.331441i | 0.986173 | + | 0.165720i | \(0.0529949\pi\) | ||||
−0.986173 | + | 0.165720i | \(0.947005\pi\) | |||||||
\(464\) | 1920.00 | 0.192099 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −876.000 | −0.0870814 | ||||||||
\(467\) | 1923.00i | 0.190548i | 0.995451 | + | 0.0952739i | \(0.0303727\pi\) | ||||
−0.995451 | + | 0.0952739i | \(0.969627\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2152.00 | −0.211877 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3552.00i | 0.346386i | ||||||||
\(473\) | 7476.00i | 0.726738i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1488.00 | 0.143282 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12828.0i | 1.22749i | ||||||||
\(479\) | −15246.0 | −1.45430 | −0.727148 | − | 0.686481i | \(-0.759154\pi\) | ||||
−0.727148 | + | 0.686481i | \(0.759154\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5240.00 | −0.496722 | ||||||||
\(482\) | 6862.00i | 0.648455i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1732.00 | −0.162660 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8206.00i | 0.763551i | 0.924255 | + | 0.381776i | \(0.124687\pi\) | ||||
−0.924255 | + | 0.381776i | \(0.875313\pi\) | |||||||
\(488\) | − 1768.00i | − 0.164003i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16806.0 | −1.54469 | −0.772346 | − | 0.635202i | \(-0.780917\pi\) | ||||
−0.772346 | + | 0.635202i | \(0.780917\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11160.0i | 1.01952i | ||||||||
\(494\) | 2360.00 | 0.214942 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 752.000 | 0.0680762 | ||||||||
\(497\) | − 2760.00i | − 0.249100i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5425.00 | 0.486686 | 0.243343 | − | 0.969940i | \(-0.421756\pi\) | ||||
0.243343 | + | 0.969940i | \(0.421756\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 14616.0i | − 1.29949i | ||||||||
\(503\) | − 19665.0i | − 1.74318i | −0.490236 | − | 0.871589i | \(-0.663090\pi\) | ||||
0.490236 | − | 0.871589i | \(-0.336910\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −756.000 | −0.0664196 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2744.00i | 0.239656i | ||||||||
\(509\) | 14724.0 | 1.28218 | 0.641090 | − | 0.767466i | \(-0.278482\pi\) | ||||
0.641090 | + | 0.767466i | \(0.278482\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4504.00 | 0.389912 | ||||||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7458.00 | 0.639997 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 6048.00i | − 0.514489i | ||||||||
\(518\) | − 2096.00i | − 0.177786i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2058.00 | 0.173057 | 0.0865284 | − | 0.996249i | \(-0.472423\pi\) | ||||
0.0865284 | + | 0.996249i | \(0.472423\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11912.0i | 0.995938i | 0.867195 | + | 0.497969i | \(0.165921\pi\) | ||||
−0.867195 | + | 0.497969i | \(0.834079\pi\) | |||||||
\(524\) | −456.000 | −0.0380161 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3912.00 | −0.324280 | ||||||||
\(527\) | 4371.00i | 0.361297i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12086.0 | 0.993343 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 944.000i | 0.0769316i | ||||||||
\(533\) | − 2520.00i | − 0.204790i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4304.00 | 0.346837 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1980.00i | 0.158669i | ||||||||
\(539\) | −13734.0 | −1.09752 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5170.00 | −0.410861 | −0.205430 | − | 0.978672i | \(-0.565859\pi\) | ||||
−0.205430 | + | 0.978672i | \(0.565859\pi\) | |||||||
\(542\) | 16990.0i | 1.34646i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2976.00 | −0.234550 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4186.00i | 0.327204i | 0.986526 | + | 0.163602i | \(0.0523112\pi\) | ||||
−0.986526 | + | 0.163602i | \(0.947689\pi\) | |||||||
\(548\) | − 636.000i | − 0.0495777i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7080.00 | −0.547401 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 2660.00i | − 0.204547i | ||||||||
\(554\) | −2732.00 | −0.209515 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9104.00 | 0.694417 | ||||||||
\(557\) | − 13026.0i | − 0.990896i | −0.868637 | − | 0.495448i | \(-0.835004\pi\) | ||||
0.868637 | − | 0.495448i | \(-0.164996\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3560.00 | 0.269359 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 11040.0i | − 0.828638i | ||||||||
\(563\) | − 10668.0i | − 0.798584i | −0.916824 | − | 0.399292i | \(-0.869256\pi\) | ||||
0.916824 | − | 0.399292i | \(-0.130744\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10876.0 | −0.807690 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5520.00i | 0.407771i | ||||||||
\(569\) | 15372.0 | 1.13256 | 0.566281 | − | 0.824212i | \(-0.308382\pi\) | ||||
0.566281 | + | 0.824212i | \(0.308382\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14989.0 | −1.09855 | −0.549273 | − | 0.835643i | \(-0.685095\pi\) | ||||
−0.549273 | + | 0.835643i | \(0.685095\pi\) | |||||||
\(572\) | 3360.00i | 0.245610i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1008.00 | 0.0732981 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1066.00i | 0.0769119i | 0.999260 | + | 0.0384559i | \(0.0122439\pi\) | ||||
−0.999260 | + | 0.0384559i | \(0.987756\pi\) | |||||||
\(578\) | − 7472.00i | − 0.537706i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 300.000 | 0.0214219 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31122.0i | 2.21088i | ||||||||
\(584\) | −9008.00 | −0.638277 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16506.0 | −1.16358 | ||||||||
\(587\) | 621.000i | 0.0436651i | 0.999762 | + | 0.0218325i | \(0.00695007\pi\) | ||||
−0.999762 | + | 0.0218325i | \(0.993050\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2773.00 | −0.193989 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4192.00i | 0.291031i | ||||||||
\(593\) | − 20187.0i | − 1.39794i | −0.715149 | − | 0.698972i | \(-0.753641\pi\) | ||||
0.715149 | − | 0.698972i | \(-0.246359\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5592.00 | 0.384324 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 360.000i | 0.0246179i | ||||||||
\(599\) | 18228.0 | 1.24337 | 0.621683 | − | 0.783269i | \(-0.286449\pi\) | ||||
0.621683 | + | 0.783269i | \(0.286449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11743.0 | −0.797017 | −0.398508 | − | 0.917165i | \(-0.630472\pi\) | ||||
−0.398508 | + | 0.917165i | \(0.630472\pi\) | |||||||
\(602\) | 1424.00i | 0.0964085i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10496.0 | −0.707080 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24418.0i | 1.63278i | 0.577503 | + | 0.816389i | \(0.304027\pi\) | ||||
−0.577503 | + | 0.816389i | \(0.695973\pi\) | |||||||
\(608\) | − 1888.00i | − 0.125935i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2880.00 | −0.190691 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2672.00i | 0.176054i | 0.996118 | + | 0.0880270i | \(0.0280562\pi\) | ||||
−0.996118 | + | 0.0880270i | \(0.971944\pi\) | |||||||
\(614\) | 18580.0 | 1.22122 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1344.00 | −0.0879080 | ||||||||
\(617\) | 8601.00i | 0.561205i | 0.959824 | + | 0.280602i | \(0.0905342\pi\) | ||||
−0.959824 | + | 0.280602i | \(0.909466\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21308.0 | −1.38359 | −0.691794 | − | 0.722095i | \(-0.743179\pi\) | ||||
−0.691794 | + | 0.722095i | \(0.743179\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16224.0i | 1.04586i | ||||||||
\(623\) | − 4344.00i | − 0.279356i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 15800.0 | 1.00878 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 1576.00i | − 0.100142i | ||||||||
\(629\) | −24366.0 | −1.54457 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19015.0 | −1.19964 | −0.599822 | − | 0.800134i | \(-0.704762\pi\) | ||||
−0.599822 | + | 0.800134i | \(0.704762\pi\) | |||||||
\(632\) | 5320.00i | 0.334839i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8838.00 | 0.553631 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6540.00i | 0.406788i | ||||||||
\(638\) | − 10080.0i | − 0.625503i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4416.00 | −0.272108 | −0.136054 | − | 0.990701i | \(-0.543442\pi\) | ||||
−0.136054 | + | 0.990701i | \(0.543442\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7580.00i | 0.464893i | 0.972609 | + | 0.232446i | \(0.0746730\pi\) | ||||
−0.972609 | + | 0.232446i | \(0.925327\pi\) | |||||||
\(644\) | −144.000 | −0.00881117 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10974.0 | 0.668369 | ||||||||
\(647\) | 14901.0i | 0.905439i | 0.891653 | + | 0.452719i | \(0.149546\pi\) | ||||
−0.891653 | + | 0.452719i | \(0.850454\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18648.0 | 1.12789 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13384.0i | 0.803923i | ||||||||
\(653\) | 12915.0i | 0.773971i | 0.922086 | + | 0.386985i | \(0.126484\pi\) | ||||
−0.922086 | + | 0.386985i | \(0.873516\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2016.00 | −0.119987 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 1152.00i | − 0.0682517i | ||||||||
\(659\) | −28128.0 | −1.66269 | −0.831344 | − | 0.555758i | \(-0.812428\pi\) | ||||
−0.831344 | + | 0.555758i | \(0.812428\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8362.00 | −0.492049 | −0.246024 | − | 0.969264i | \(-0.579124\pi\) | ||||
−0.246024 | + | 0.969264i | \(0.579124\pi\) | |||||||
\(662\) | − 16400.0i | − 0.962846i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −600.000 | −0.0350670 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1080.00i | − 0.0626953i | ||||||||
\(668\) | 5964.00i | 0.345440i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9282.00 | −0.534020 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29708.0i | 1.70157i | 0.525511 | + | 0.850787i | \(0.323874\pi\) | ||||
−0.525511 | + | 0.850787i | \(0.676126\pi\) | |||||||
\(674\) | −19112.0 | −1.09224 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7188.00 | −0.408967 | ||||||||
\(677\) | − 6762.00i | − 0.383877i | −0.981407 | − | 0.191939i | \(-0.938523\pi\) | ||||
0.981407 | − | 0.191939i | \(-0.0614774\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6176.00 | 0.349062 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 3948.00i | − 0.221667i | ||||||||
\(683\) | − 19155.0i | − 1.07313i | −0.843860 | − | 0.536563i | \(-0.819722\pi\) | ||||
0.843860 | − | 0.536563i | \(-0.180278\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5360.00 | −0.298317 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 2848.00i | − 0.157818i | ||||||||
\(689\) | 14820.0 | 0.819444 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22975.0 | −1.26485 | −0.632424 | − | 0.774622i | \(-0.717940\pi\) | ||||
−0.632424 | + | 0.774622i | \(0.717940\pi\) | |||||||
\(692\) | 9612.00i | 0.528025i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20232.0 | 1.10662 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 11718.0i | − 0.636802i | ||||||||
\(698\) | 13502.0i | 0.732175i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6450.00 | −0.347522 | −0.173761 | − | 0.984788i | \(-0.555592\pi\) | ||||
−0.173761 | + | 0.984788i | \(0.555592\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 15458.0i | − 0.829317i | ||||||||
\(704\) | 2688.00 | 0.143903 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8124.00 | −0.433075 | ||||||||
\(707\) | 528.000i | 0.0280870i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34538.0 | −1.82948 | −0.914740 | − | 0.404042i | \(-0.867605\pi\) | ||||
−0.914740 | + | 0.404042i | \(0.867605\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8688.00i | 0.457299i | ||||||||
\(713\) | − 423.000i | − 0.0222181i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10560.0 | 0.551181 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 17556.0i | − 0.912513i | ||||||||
\(719\) | −27114.0 | −1.40637 | −0.703186 | − | 0.711006i | \(-0.748240\pi\) | ||||
−0.703186 | + | 0.711006i | \(0.748240\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3568.00 | 0.184299 | ||||||||
\(722\) | − 6756.00i | − 0.348244i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4292.00 | −0.220319 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 236.000i | − 0.0120396i | −0.999982 | − | 0.00601978i | \(-0.998084\pi\) | ||||
0.999982 | − | 0.00601978i | \(-0.00191617\pi\) | |||||||
\(728\) | 640.000i | 0.0325824i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16554.0 | 0.837581 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27128.0i | 1.36698i | 0.729960 | + | 0.683489i | \(0.239538\pi\) | ||||
−0.729960 | + | 0.683489i | \(0.760462\pi\) | |||||||
\(734\) | 1912.00 | 0.0961488 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 288.000 | 0.0144237 | ||||||||
\(737\) | − 22596.0i | − 1.12935i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5249.00 | −0.261282 | −0.130641 | − | 0.991430i | \(-0.541704\pi\) | ||||
−0.130641 | + | 0.991430i | \(0.541704\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5928.00i | 0.293293i | ||||||||
\(743\) | 13896.0i | 0.686130i | 0.939312 | + | 0.343065i | \(0.111465\pi\) | ||||
−0.939312 | + | 0.343065i | \(0.888535\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4600.00 | −0.225761 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 15624.0i | 0.763730i | ||||||||
\(749\) | 4560.00 | 0.222455 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27665.0 | 1.34422 | 0.672111 | − | 0.740451i | \(-0.265388\pi\) | ||||
0.672111 | + | 0.740451i | \(0.265388\pi\) | |||||||
\(752\) | 2304.00i | 0.111726i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4800.00 | −0.231838 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8122.00i | 0.389959i | 0.980807 | + | 0.194980i | \(0.0624641\pi\) | ||||
−0.980807 | + | 0.194980i | \(0.937536\pi\) | |||||||
\(758\) | − 58.0000i | − 0.00277923i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10584.0 | 0.504165 | 0.252083 | − | 0.967706i | \(-0.418885\pi\) | ||||
0.252083 | + | 0.967706i | \(0.418885\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6940.00i | 0.329286i | ||||||||
\(764\) | 5880.00 | 0.278444 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16254.0 | −0.766685 | ||||||||
\(767\) | − 8880.00i | − 0.418042i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18619.0 | 0.873106 | 0.436553 | − | 0.899679i | \(-0.356199\pi\) | ||||
0.436553 | + | 0.899679i | \(0.356199\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18880.0i | 0.880189i | ||||||||
\(773\) | 22251.0i | 1.03533i | 0.855582 | + | 0.517667i | \(0.173199\pi\) | ||||
−0.855582 | + | 0.517667i | \(0.826801\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12352.0 | −0.571406 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15876.0i | 0.731597i | ||||||||
\(779\) | 7434.00 | 0.341914 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28980.0 | 1.32777 | ||||||||
\(782\) | 1674.00i | 0.0765500i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5232.00 | 0.238338 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 24854.0i | − 1.12573i | −0.826549 | − | 0.562865i | \(-0.809699\pi\) | ||||
0.826549 | − | 0.562865i | \(-0.190301\pi\) | |||||||
\(788\) | 3060.00i | 0.138335i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5736.00 | −0.257837 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4420.00i | 0.197930i | ||||||||
\(794\) | 544.000 | 0.0243147 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2672.00 | 0.118978 | ||||||||
\(797\) | − 3681.00i | − 0.163598i | −0.996649 | − | 0.0817991i | \(-0.973933\pi\) | ||||
0.996649 | − | 0.0817991i | \(-0.0260666\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13392.0 | −0.592960 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9108.00i | 0.401016i | ||||||||
\(803\) | 47292.0i | 2.07833i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1880.00 | −0.0821590 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 1056.00i | − 0.0459777i | ||||||||
\(809\) | 5142.00 | 0.223465 | 0.111732 | − | 0.993738i | \(-0.464360\pi\) | ||||
0.111732 | + | 0.993738i | \(0.464360\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18484.0 | −0.800322 | −0.400161 | − | 0.916445i | \(-0.631046\pi\) | ||||
−0.400161 | + | 0.916445i | \(0.631046\pi\) | |||||||
\(812\) | − 1920.00i | − 0.0829788i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22008.0 | 0.947641 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10502.0i | 0.449717i | ||||||||
\(818\) | − 2002.00i | − 0.0855725i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25014.0 | 1.06333 | 0.531665 | − | 0.846954i | \(-0.321566\pi\) | ||||
0.531665 | + | 0.846954i | \(0.321566\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 32146.0i | − 1.36153i | −0.732502 | − | 0.680765i | \(-0.761648\pi\) | ||||
0.732502 | − | 0.680765i | \(-0.238352\pi\) | |||||||
\(824\) | −7136.00 | −0.301692 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3552.00 | 0.149625 | ||||||||
\(827\) | 10977.0i | 0.461557i | 0.973006 | + | 0.230779i | \(0.0741273\pi\) | ||||
−0.973006 | + | 0.230779i | \(0.925873\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36602.0 | −1.53346 | −0.766731 | − | 0.641969i | \(-0.778118\pi\) | ||||
−0.766731 | + | 0.641969i | \(0.778118\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 1280.00i | − 0.0533366i | ||||||||
\(833\) | 30411.0i | 1.26492i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −9912.00 | −0.410064 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3588.00i | 0.147906i | ||||||||
\(839\) | −11076.0 | −0.455764 | −0.227882 | − | 0.973689i | \(-0.573180\pi\) | ||||
−0.227882 | + | 0.973689i | \(0.573180\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9989.00 | −0.409570 | ||||||||
\(842\) | − 32258.0i | − 1.32029i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −18404.0 | −0.750583 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1732.00i | 0.0702624i | ||||||||
\(848\) | − 11856.0i | − 0.480114i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2358.00 | 0.0949838 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36848.0i | 1.47908i | 0.673115 | + | 0.739538i | \(0.264956\pi\) | ||||
−0.673115 | + | 0.739538i | \(0.735044\pi\) | |||||||
\(854\) | −1768.00 | −0.0708428 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9120.00 | −0.364153 | ||||||||
\(857\) | 26961.0i | 1.07464i | 0.843377 | + | 0.537322i | \(0.180564\pi\) | ||||
−0.843377 | + | 0.537322i | \(0.819436\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 415.000 | 0.0164838 | 0.00824192 | − | 0.999966i | \(-0.497376\pi\) | ||||
0.00824192 | + | 0.999966i | \(0.497376\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 26712.0i | − 1.05547i | ||||||||
\(863\) | − 45501.0i | − 1.79475i | −0.441265 | − | 0.897377i | \(-0.645470\pi\) | ||||
0.441265 | − | 0.897377i | \(-0.354530\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 23000.0 | 0.902508 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 752.000i | − 0.0294062i | ||||||||
\(869\) | 27930.0 | 1.09029 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10760.0 | −0.418586 | ||||||||
\(872\) | − 13880.0i | − 0.539032i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1062.00 | −0.0411015 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 35042.0i | − 1.34924i | −0.738165 | − | 0.674620i | \(-0.764307\pi\) | ||||
0.738165 | − | 0.674620i | \(-0.235693\pi\) | |||||||
\(878\) | 22298.0i | 0.857085i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1080.00 | 0.0413009 | 0.0206505 | − | 0.999787i | \(-0.493426\pi\) | ||||
0.0206505 | + | 0.999787i | \(0.493426\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 20164.0i | − 0.768485i | −0.923232 | − | 0.384243i | \(-0.874463\pi\) | ||||
0.923232 | − | 0.384243i | \(-0.125537\pi\) | |||||||
\(884\) | 7440.00 | 0.283070 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7698.00 | −0.291895 | ||||||||
\(887\) | − 20067.0i | − 0.759621i | −0.925064 | − | 0.379811i | \(-0.875989\pi\) | ||||
0.925064 | − | 0.379811i | \(-0.124011\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2744.00 | 0.103522 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8632.00i | 0.324014i | ||||||||
\(893\) | − 8496.00i | − 0.318374i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 512.000 | 0.0190901 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 36096.0i | − 1.34136i | ||||||||
\(899\) | 5640.00 | 0.209238 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 68913.0 | 2.54809 | ||||||||
\(902\) | 10584.0i | 0.390697i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11472.0 | 0.422072 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26524.0i | 0.971020i | 0.874231 | + | 0.485510i | \(0.161366\pi\) | ||||
−0.874231 | + | 0.485510i | \(0.838634\pi\) | |||||||
\(908\) | − 12492.0i | − 0.456566i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35568.0 | 1.29355 | 0.646773 | − | 0.762683i | \(-0.276118\pi\) | ||||
0.646773 | + | 0.762683i | \(0.276118\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3150.00i | 0.114184i | ||||||||
\(914\) | −8528.00 | −0.308623 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8108.00 | 0.292463 | ||||||||
\(917\) | 456.000i | 0.0164214i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23704.0 | 0.850841 | 0.425420 | − | 0.904996i | \(-0.360126\pi\) | ||||
0.425420 | + | 0.904996i | \(0.360126\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 20484.0i | − 0.731675i | ||||||||
\(923\) | − 13800.0i | − 0.492126i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6604.00 | −0.234364 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3840.00i | 0.135834i | ||||||||
\(929\) | 40590.0 | 1.43349 | 0.716746 | − | 0.697334i | \(-0.245631\pi\) | ||||
0.716746 | + | 0.697334i | \(0.245631\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19293.0 | −0.679165 | ||||||||
\(932\) | − 1752.00i | − 0.0615758i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3846.00 | −0.134738 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12964.0i | 0.451991i | 0.974128 | + | 0.225995i | \(0.0725634\pi\) | ||||
−0.974128 | + | 0.225995i | \(0.927437\pi\) | |||||||
\(938\) | − 4304.00i | − 0.149819i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29922.0 | 1.03659 | 0.518294 | − | 0.855203i | \(-0.326567\pi\) | ||||
0.518294 | + | 0.855203i | \(0.326567\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1134.00i | 0.0391603i | ||||||||
\(944\) | −7104.00 | −0.244932 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14952.0 | −0.513881 | ||||||||
\(947\) | − 5241.00i | − 0.179841i | −0.995949 | − | 0.0899206i | \(-0.971339\pi\) | ||||
0.995949 | − | 0.0899206i | \(-0.0286613\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22520.0 | 0.770316 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2976.00i | 0.101316i | ||||||||
\(953\) | 26214.0i | 0.891033i | 0.895274 | + | 0.445517i | \(0.146980\pi\) | ||||
−0.895274 | + | 0.445517i | \(0.853020\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −25656.0 | −0.867965 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 30492.0i | − 1.02834i | ||||||||
\(959\) | −636.000 | −0.0214155 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27582.0 | −0.925850 | ||||||||
\(962\) | − 10480.0i | − 0.351236i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13724.0 | −0.458527 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 18278.0i | − 0.607840i | −0.952698 | − | 0.303920i | \(-0.901705\pi\) | ||||
0.952698 | − | 0.303920i | \(-0.0982955\pi\) | |||||||
\(968\) | − 3464.00i | − 0.115018i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24942.0 | −0.824333 | −0.412166 | − | 0.911109i | \(-0.635228\pi\) | ||||
−0.412166 | + | 0.911109i | \(0.635228\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 9104.00i | − 0.299960i | ||||||||
\(974\) | −16412.0 | −0.539912 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3536.00 | 0.115968 | ||||||||
\(977\) | 11226.0i | 0.367607i | 0.982963 | + | 0.183803i | \(0.0588409\pi\) | ||||
−0.982963 | + | 0.183803i | \(0.941159\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45612.0 | 1.48904 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 33612.0i | − 1.09226i | ||||||||
\(983\) | − 23073.0i | − 0.748641i | −0.927299 | − | 0.374321i | \(-0.877876\pi\) | ||||
0.927299 | − | 0.374321i | \(-0.122124\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −22320.0 | −0.720906 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4720.00i | 0.151987i | ||||||||
\(989\) | −1602.00 | −0.0515072 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22037.0 | 0.706386 | 0.353193 | − | 0.935551i | \(-0.385096\pi\) | ||||
0.353193 | + | 0.935551i | \(0.385096\pi\) | |||||||
\(992\) | 1504.00i | 0.0481371i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5520.00 | 0.176141 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 19082.0i | − 0.606151i | −0.952966 | − | 0.303076i | \(-0.901986\pi\) | ||||
0.952966 | − | 0.303076i | \(-0.0980135\pi\) | |||||||
\(998\) | 10850.0i | 0.344139i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1350.4.c.d.649.2 | 2 | ||
3.2 | odd | 2 | 1350.4.c.q.649.1 | 2 | |||
5.2 | odd | 4 | 270.4.a.e.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 1350.4.a.u.1.1 | 1 | |||
5.4 | even | 2 | inner | 1350.4.c.d.649.1 | 2 | ||
15.2 | even | 4 | 270.4.a.i.1.1 | yes | 1 | ||
15.8 | even | 4 | 1350.4.a.g.1.1 | 1 | |||
15.14 | odd | 2 | 1350.4.c.q.649.2 | 2 | |||
20.7 | even | 4 | 2160.4.a.o.1.1 | 1 | |||
45.2 | even | 12 | 810.4.e.h.271.1 | 2 | |||
45.7 | odd | 12 | 810.4.e.q.271.1 | 2 | |||
45.22 | odd | 12 | 810.4.e.q.541.1 | 2 | |||
45.32 | even | 12 | 810.4.e.h.541.1 | 2 | |||
60.47 | odd | 4 | 2160.4.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
270.4.a.e.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
270.4.a.i.1.1 | yes | 1 | 15.2 | even | 4 | ||
810.4.e.h.271.1 | 2 | 45.2 | even | 12 | |||
810.4.e.h.541.1 | 2 | 45.32 | even | 12 | |||
810.4.e.q.271.1 | 2 | 45.7 | odd | 12 | |||
810.4.e.q.541.1 | 2 | 45.22 | odd | 12 | |||
1350.4.a.g.1.1 | 1 | 15.8 | even | 4 | |||
1350.4.a.u.1.1 | 1 | 5.3 | odd | 4 | |||
1350.4.c.d.649.1 | 2 | 5.4 | even | 2 | inner | ||
1350.4.c.d.649.2 | 2 | 1.1 | even | 1 | trivial | ||
1350.4.c.q.649.1 | 2 | 3.2 | odd | 2 | |||
1350.4.c.q.649.2 | 2 | 15.14 | odd | 2 | |||
2160.4.a.e.1.1 | 1 | 60.47 | odd | 4 | |||
2160.4.a.o.1.1 | 1 | 20.7 | even | 4 |